PDE
Calculations
4/24/2001
1.
Flow control equations:
Axis-symmetric Euler equations + one species equation.
2. Numerical method: CE/SE method
3.
Computational Domain: [0, 12.6ft]
x [-4.6, 4.6ft]
(Because of symmetry, only up half of the domain is calculated)
4.
Mesh: 290360 cells
(Inside and near thrust tube,
the mesh is uniform; the others are stretching)
5.
Boundary conditions:
--
On solid wall and symmetric line, reflective boundary condition is used.
-- On outlet and open surface, non-reflective boundary condition is used.
6.
Flow conditions:
Chamber temperature T=510R; Chamber
pressure P=15.0 Psia;
Equivalence ratio F=1.3;
Freq.=60 Hz
C-J detonation velocity VC-J=6200ft/sec.;
Pressure jump P2/P1=16.667.
Diameter of tube = 5inches, and its length =26.138inches.
7.
Schematic of point locations where numerical data are taken.
Click cyan or blue semi-ball in following picture to get corresponding pressure or density curve.
(1). Line L-1 is located 5 7/8 inches below the PDE centerline. There are ten points located on it, and their distances are (from the left side):
| Point-1: | 4 inches | |
| Point-2: | 5.66 inches | |
| Point-3: | 8 inches | |
| Point-4: | 11.32 inches | |
| Point-5: | 16 inches | |
| Point-6: | 22.64 inches | |
| Point-7: | 32 inches | |
| Point-8: | 45.28 inches | |
| Point-9: | 64 inches | |
| Point-10: | 90.56 inches |
(2).
L-2, L-3 and L-4 are the rotating ones of L-1 at 30o, 60o,
and 90o respectively.
8. Numerical results (multi-cycle):
(1). Pressure history on left thrust tube wall.
(2). Pressures and densities of ten locations on the first line (q = 0o).
| Pressures | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 | Point-9 | Point-10 | |
| Densities | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 | Point-9 | Point-10 |
(3). Pressures and densities of ten locations on the second line (q = 30o).
| Pressures | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 | Point-9 | Point-10 | |
| Densities | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 | Point-9 | Point-10 |
(4). Pressures and densities of eight locations on the third line (q = 60o).
| Pressures | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 | |||
| Densities | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 |
(5). Pressures and densities of seven locations on the fourth line (q = 90o).
| Pressures | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 | |||
| Densities | Point-1 | Point-2 | Point-3 | Point-4 | Point-5 | Point-6 | Point-7 | Point-8 |
9.
Remarks:
(1).
Fine mesh (larger domain) will be used in our parallel computations.
(2). Multi-cycle calculations.
(3). Better data analysis method.
(4). Improve chemical reaction models.
(5). 3D calculations.
